Single-cycle pulses with multimillion volts per centimeter field strengths and spectra in the terahertz (THz) band have attracted great interest due to their ability to coherently manipulate molecular orientations and electron spins resonantly and nonresonantly. The tremendous progress made in the development of compact and powerful terahertz sources have identified intense laser-thin foil interaction as a potential candidate for high-power broadband terahertz radiation. They are micrometers in size and deliver radially polarized terahertz pulses with millijoule energy and gigawatt peak power. Although several works have been carried out to investigate the terahertz generation process, their origin and angular distribution are still debated. We present here an indisputable study on their spatiotemporal characteristics and elaborate the underlying physical processes via recording the three-dimensional beam profile along with transient dynamics. These results are substructured with the quantitative visualization of the charge particle spectra.